Unit Roots, Cointegration, and Structural Change (Themes in Modern Econometrics)

Cover......Page 1
Frontmatter......Page 2
Contents......Page 8
Figures......Page 13
Tables......Page 14
Dedication......Page 16
Preface......Page 18
Part I - Introduction and basic concepts......Page 20
1 - Introduction......Page 22
References......Page 25
2.1 Stochastic processes......Page 27
2.2 Some commonly used stationary models......Page 30
2.3 Box-Jenkins methods......Page 36
2.4 Integrated variables and cointegration......Page 39
2.5 Spurious regression......Page 47
2.6 Deterministic trend and stochastic trend......Page 48
2.7 Detrending methods......Page 51
2.8 VAR, ECM, and ADL......Page 53
2.9 Unit root tests......Page 56
2.10 Cointegration tests and ECM......Page 58
2.11 Summary......Page 60
References......Page 61
Part II - Unit roots and cointegration......Page 64
3.1 Introduction......Page 66
3.2 Unit roots and Wiener processes......Page 68
3.3 Unit root tests without a deterministic trend......Page 79
3.4 DF test with a linear deterministic trend......Page 84
3.5 Specification of deterministic trends......Page 91
3.6 Unit root tests for a wide class of errors......Page 93
3.7 Sargan-Bhargava and Bhargava tests......Page 101
3.8 Variance ratio tests......Page 105
3.9 Tests for TSP versus DSP......Page 106
3.10 Forecasting from TS versus DS models......Page 108
References......Page 111
4.1 Introduction......Page 117
4.2 Size distortion and low power of unit root tests......Page 119
4.3 Solutions to the problems of size and power......Page 122
4.4 Problem of overdifferencing: MA roots......Page 135
4.5 Tests with stationarity as null......Page 139
4.6 Confirmatory analysis......Page 145
4.7 Frequency of observations and power of unit root tests......Page 148
4.8 Other types of nonstationarity......Page 150
4.9 Panel data unit root tests......Page 152
4.10 Uncertain unit roots and the pre-testing problem......Page 158
4.11 Other unit root tests......Page 159
4.12 Median-unbiased estimation......Page 160
4.13 Summary and conclusions......Page 164
References......Page 165
5.2 A general CI system......Page 174
5.3 A two-variable model: Engle-Granger methods......Page 175
5.4 A triangular system......Page 179
5.5 System estimation methods......Page 184
5.6 The identification problem......Page 192
5.7 Finite sample evidence......Page 194
5.8 Forecasting in cointegrated systems......Page 203
5.9 Miscellaneous other problems......Page 206
References......Page 210
6.2 Single equation methods: residual-based tests......Page 217
6.3 Single equation methods: ECM tests......Page 222
6.4 Tests with cointegration as null......Page 224
6.5 Multiple equation methods......Page 230
6.6 Cointegration tests based on LCCA......Page 241
6.7 Other tests for cointegration......Page 245
6.8 Miscellaneous other problems......Page 247
6.9 Of what use are cointegration tests?......Page 252
6.10 Conclusions......Page 260
References......Page 261
7.1 I(1) regressors not cointegrated......Page 268
7.2 I(1) regressors cointegrated......Page 269
7.3 Unbalanced equations......Page 270
7.4 Lagged dependent variables: the ARDL model......Page 271
7.5 Uncertain unit roots......Page 273
7.6 Uncertain unit roots and cointegration......Page 275
References......Page 277
Part III - Extensions of the basic model......Page 280
8 - The Bayesian analysis of stochastic trends......Page 282
8.1 Introduction to Bayesian inference......Page 283
8.2 The posterior distribution of an autoregressive parameter......Page 285
8.3 Bayesian inference on the Nelson-Plosser data......Page 287
8.4 The debate on the appropriate prior......Page 290
8.6 Priors and time units of measurement......Page 296
8.7 On testing point null hypotheses......Page 297
8.8 Further comments on prior distributions......Page 303
8.9 Bayesian inference on cointegrated systems......Page 306
8.10 Bayesian long-run prediction......Page 309
8.11 Conclusion......Page 310
References......Page 311
9.1 Some definitions......Page 315
9.2 Unit root tests against fractional alternatives......Page 317
9.3 Estimation of ARFIMA models......Page 319
9.4 Estimation of fractionally cointegrated models......Page 321
9.5 Empirical relevance of fractional unit roots......Page 322
9.6 Summary and conclusions......Page 324
References......Page 325
10.2 A review of the bootstrap approach......Page 328
10.3 The AR(1) model......Page 341
10.4 Bootstrapping unit root tests......Page 344
10.5 The moving block bootstrap and extensions......Page 347
10.6 Issues in bootstrapping cointegrating regressions......Page 351
10.7 Miscellaneous other applications......Page 354
References......Page 355
11.1 Determination of the order of differencing......Page 361
11.2 Cointegration analysis with I(2) and I(1) variables......Page 367
11.3 Empirical applications......Page 374
11.4 Summary and conclusions......Page 377
References......Page 378
12 - Seasonal unit roots and seasonal cointegration......Page 381
12.1 Effect of seasonal adjustment......Page 383
12.2 Seasonal integration......Page 384
12.3 Tests for seasonal unit roots......Page 385
12.4 The unobserved component model......Page 390
12.5 Seasonal cointegration......Page 394
12.6 Estimation of seasonally cointegrated systems......Page 395
12.7 Empirical evidence......Page 397
12.8 Periodic autoregression and periodic integration......Page 398
12.10 Time aggregation and systematic sampling......Page 400
12.11 Conclusion......Page 401
References......Page 402
Part IV - Structural change......Page 406
13 - Structural change, unit roots, and cointegration......Page 408
13.2 Tests with known break points......Page 409
13.3 Tests with unknown break points......Page 410
13.4 A summary assessment......Page 417
13.5 Tests for unit roots under structural change......Page 418
13.6 The Bayesian approach......Page 421
13.7 A summary assessment of the empirical work......Page 426
13.8 Effect of structural change on cointegration tests......Page 429
13.9 Tests for structural change in cointegrated relationships......Page 430
13.10 Miscellaneous other issues......Page 433
13.11 Practical conclusions......Page 435
References......Page 437
14.2 Different types of outliers in time series models......Page 444
14.3 Effects of outliers on unit root tests......Page 447
14.4 Outlier detection......Page 456
14.5 Robust unit root tests......Page 459
14.6 Robust estimation of cointegrating regressions......Page 464
14.8 Conclusions......Page 467
References......Page 468
15.1 The switching regression model......Page 473
15.2 The Markov switching regression model......Page 474
15.3 The Hamilton model......Page 476
15.4 On the usefulness of the MSR model......Page 479
15.5 Extensions of the MSR model......Page 482
15.6 Gradual regime switching models......Page 485
15.7 A model with parameters following a random walk......Page 488
15.8 A general state-space model......Page 489
15.9 Derivation of the Kalman filter......Page 491
15.10 Harvey's structural time series model (1989)......Page 494
15.11 Further comments on structural time series models......Page 496
References......Page 498
16 - Future directions......Page 505
References......Page 507
Appendix 1 - A brief guide to asymptotic theory......Page 509
Author index......Page 511
Subject index......Page 519